Demonstration of Quadrature Squeezed Surface-Plasmons in a Gold Waveguide

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by  Alexander Huck

Demonstration of Quadrature Squeezed Surface-Plasmons in a Gold Waveguide
Alexander Huck,1,∗ Stephan Smolka,2 Peter Lodahl,2 Anders S. Sørensen,3
Alexandra Boltasseva,2,4 Jiri Janousek,1 and Ulrik L. Andersen1,†
1Department of Physics, Technical University of Denmark, Building 309, 2800 Lyngby, Denmark
2DTU Fotonik, Department of Photonics Engineering,
Technical University of Denmark, Ørsted Plads 343, 2800 Lyngby, Denmark
3QUANTOP, Danish Quantum Optics Center and Niels Bohr Institute, 2100 Copenhagen, Denmark
4Birck Nanotechnology Center, Purdue University, West Lafayette 47907, IN, USA
(Dated: January 26, 2009)
Wereportontheefficientgeneration,propagation,andre-emissionofsqueezedlong-rangesurface-
plasmon polaritons (SPPs) in a gold waveguide. Squeezed light is used to excite the non-classical
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SPPs and the re-emitted quantum state is fully quantum characterized by complete tomographic
0
reconstructionofthedensitymatrix. Wefindthattheplasmon-assistedtransmissionofnon-classical
0
light in metallic waveguides can be described by a Hamiltonian analogue to a beam splitter. This
2
result is explained theoretically.

n
a PACSnumbers: 03.67.-a,42.50.Lc,42.50.Nn,73.20.Mf
J

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2 Enormous interest has recently been devoted to the density matrix. This is in strong contrast to previous
emergent field of quantum plasmonics due to its unique experiments on plasmon assisted quantum state trans-
]
h capabilities in the way electromagnetic radiation can be mission, where only a certain property of the quantum
p localized and manipulated at the nanoscale. In partic- state was investigated.
- ular, integrated quantum technologies based on surface
t SPPs are combined electron oscillations and electro-
n plasmons hold great promises for quantum information
magnetic waves propagating along the interface between
a
processing,sinceitallowsforscalability,miniaturization,
u a conductor and a dielectric medium [8]. By reducing
and coherent coupling to single emitters [1, 2, 3, 4, 5].
q the thickness of the metal film the SPP from the upper
[ To enable these quantum information processing tech- interface and the lower interface can couple. This cou-

1 nologies with high fidelity, it is of paramount impor- pling results in the formation of either long-range (LR)
tance, that the nonclassicality of the plasmonic modes
v SPPsorshort-range(SR)SPPsdependingonthe propa-
9 is preserved in propagation. The first experiment ver- gation length of the mode [8]. In general, the coupled
6 ifying the preservation of entanglement in plasmonic
LR-SPP (SR-SPP) modes are characterized by an in-
9 nanostructureswascarriedoutbyAlterwischeretal.[6].
creased (decreased) propagation length compared to a
3
They demonstrated the survival of polarization entan-
SPPpropagatingalongasingleinterface. LR-SPPs(SR-
.
1 glement after plasmonic propagation through subwave-
SPPs) are further characterized by a symmetric (anti-
0 length holes in a metal film. The preservation of energy
symmetric) longitudinal electric field distribution, which
9
time entanglement in a perforated metal film as well as
0 allows the LR-SPPs to be efficiently excited using end-
in a thin conducting waveguide was later demonstrated
: fire coupling [9, 10].
v byFaseletal.[7]. Theseexperimentshavewitnessedthe
i A sketch of the sample as well as the experimental
X preservation of probabilistically prepared entanglement
setupisshowninFig.1(a). Thesampleconsistsofagold
(thus neglecting the vacuum contribution) described in
r
stripe embedded in lossless transparent polymer Benzo-
a the two dimensional Hilbert space.
cyclobutene (BCB). It was prepared by first spinning a
In the present Letter we investigate the compatibil- 12-15µm layer of BCB onto a silicon substrate. The
ity of the quantum plasmonic technology with the con- metallic waveguide was then patterned using standard
tinuous variable quantum domain (described in the in- UVlithography,followedby golddepositionby meansof
finite dimensional Hilbert space) by demonstrating the electron beam evaporation and lift-off. Finally, another
plasmonic excitation, propagation, and detection of de- layer of BCB with a thickness of 10 µm was spun onto
terministically prepared quadrature squeezed vacuum the sample with exactly the same spinning conditions
states. We show that a squeezed vacuum state excite to ensure a symmetric dielectric environmentof the gold
an electron resonance on the surfaces of a metallic gold stripe. InFig.1(b)wepresentapowerdensityplotofthe
waveguide to form a surface plasmon polariton (SPP). LR-SPP mode in the transverse plane of the gold stripe.
Despite loss and decoherence in the plasmonic mode we Thiswasobtainedbyafiniteelementmethodsimulation
demonstratethatquadraturesqueezingisretainedinthe for the metal stripe geometry as presented in Fig. 1(a).
retrieved light state. Importantly, we fully characterize ThearrowsinFig.1(b)showthedirectionofthe electric
the input state and output state by performing a com- field vector in the transverse plane of the sample, which
plete quantum tomographic reconstruction of the states is, with respect to the metal stripe surface, transverse
2
magnetic(TM)polarized. Thisfactisinagreementwith ingawavelengthof532nm,thusproducingsqueezedlight
the analytical model for a sample of infinite width [8]. centered around 1064nm. The round trip path length of
the OPO cavity is 275mm, it has a free spectral range
of 1.1GHz, and a bandwidth of approximately 21MHz.
The out-coupling mirror has a power transmissivity of
T=10%.
Before investigating the quantum properties of a SPP,
we characterizeits classicalproperties. Forthis purpose,
we seed the OPO cavity with an auxiliary light field at
1064nmwiththeOPOpumpbeamblocked. Ahalfwave
plate is placedbetween the OPOand the goldsample to
controlthelinearpolarizationofthelightfield. Thelight
fieldisthenfocusedontothesamplewithanasphericlens
ensuring a good mode matching to the LR-SPP mode.
At maximum, we have observed a total transmission of
32.8 0.5%forTMpolarizedincidentlight. Whenrotat-
±
ing the polarization of the incident light field, the trans-
mission decreases as cos2(α), where α is the angle of the
half-wave plate with respect to the TM direction. For
α = 90◦ only scattered as well as higher order modes
are measured. This result clearly demonstrates the ex-
pectedpolarizationdependenceandthusproves,thatthe
LR-SPP mode is excited [9].
HavingestablishedtheclassicalexcitationofaSPP,we
now proceed with the analysis of non-classical SPPs. In
the following we fully characterize the quantum state of
light before it is launched into the gold stripe, and also
after transmission and re-emission. The results of the
analysis are shown in Fig. 2. For the characterizationof
the input state, the sample is removed from the setup
and the squeezed vacuum light field is measured with a
homodyne detection system, as shown in Fig. 1(a). The
FIG. 1: (Color online). (a) Sketch of the experimental setup difference signal of the two detectors is amplified, mixed
and LR-SPP sample: The sample is made of gold embedded
down at an optical sideband frequency of 4.7MHz, low
in lossless transparent BCB and its dimensions are specified
passfilteredwithabandwidthof150kHz,andfinallydig-
as written in the figure. Experimental setup: OPO - optical
itized with 8bit resolution. A quadrature measurement
parametricoscillator, PPKTP-periodicallypoledKTPcrys-
tal, SV - squeezed vacuum, λ/2 - half-wave plate, Φ - piezo set containing more than 5.5M data points is shown in
actuated mirror for phase variation, 50:50 - symmetric beam Fig. 2(a) for a rotation in phase space from 0 to 2π. By
splitter, and HD - homodyne detection scheme. (b) Normal- applying the maximum likelihood algorithm [14] on this
ized power density plot of the LR-SPP mode for sample di- dataset wereconstructthe squeezedvacuum statesden-
mensions as specified in (a). The arrows show the direction
sity matrix ρ , whose absolute values are presented in
of the electric field in the transverse plane. At the experi- in
Fig.2(b). Fromthedensitymatrixρ ,theWignerfunc-
mental wavelength of 1064nm the refractive indices of gold in
tionW(X,P)hasbeenreconstructed,whichispresented
andBCB are specified tobenAu =0.2381+i7.7199 [11]and
nBCB=1.539, which were used in the simulation. (c) Depen- inFig.2(c). For variousqudratures,the noise powercan
denceofthetotaltransmission Tontheangleαofthelinear eitherbecalculateddirectlyfromthetimeresolveddata,
polarized incident light field. α is measured with respect to as shownby the black solid line in Fig. 2(d), or from the
TM polarization and set by theλ/2 wave plate. statesdensitymatrixρ ,asshownbythereddashedline
in
in Fig. 2(d). The degree of squeezing and anti-squeezing
As a source of non-classical light we use a bow-tie arefoundtobe-1.9 0.1dBand6.1 0.1dB,respectively.
± ±
shapedopticalparametricoscillator(OPO)operatingbe- The squeezed light is then carefully injected into the
lowthreshold, seeFig. 1(a)[12]. The non-linearmedium gold stripe, thereby linearly mapping the non-classical
insidetheOPOisatype-IIIperiodicallypoledKTP(PP- photonstatisticsontoaplasmonicstate,asdescribedfor
KTP) crystal of 10mm length, which is placed at the the exciation with a single photon in Ref. [13]. Subse-
beam waistbetween two curvedhighly reflective mirrors quently, the squeezed SPP propagates through the sam-
with 25mm radius of curvature. We pump the PPKTP ple, is efficiently re-emitted at the rear end, and mea-
crystalwithafrequencydoubledNd:YAGlaserfieldhav- sured with the homodyne detector. The time resolved
3

1.00
F=0.993
0.95
y
elit
d
Fi
0.90
=0.33
0.85
0.0 0.2 0.4 0.6 0.8 1.0
FIG.3: Fidelitybetweenbeamsplittermodeρout(η)obtained
afterapplyingthebeamsplitteroperatorUˆBS(η)ontheinput
mode ρin and LR-SPP output mode ρLR−SPP versus trans-
missions η.
quadrature data are recorded similarly as was described
above and the result is shown in Fig. 2(e). From these
datawereconstructthedensitymatrixρ andthe
LR−SPP
Wigner functionW(X,P), as illustratedinFig.2(f) and
(g),respectively. Bycalculatingthequadraturevariances
(either directly from the time-resolved data or from the
density matrix) we find a minimum of -0.7 0.1dB and
±
amaximumof3.2 0.1dBwith respectto the shotnoise
±
level,asispresentedinFig.2(h). Wethereforeconclude,
that the retrieved light state is squeezed and that the
squeezing survived the plasmonic propagation.
We furthermore investigate whether the operation,
that transforms the density matrix of the input state
ρ to that of the output state ρ can be de-
in LR−SPP
scribed by the unitary beam splitter operator Uˆ =
BS
exp θ(aˆ†ˆbeiφ aˆˆb†e−iΦ) . Here, aˆ and ˆb are the field
{2 − }
operators of the beam splitter input modes, Φ is the rel-
FIG. 2: (Color online). Experimental results of the squeezed ativephasebetweenthemodesaˆandˆb,andθ islinkedto
vacuum state (input) and the quantum state after LR-SPP
the transmission η via η =cos(θ). The expected output
excitation,propagation,andreemission (output). (a)and(e) 2
Timeresolveddataforvariouselectricfieldquadratureswhile state is thus ρ (η) = Tr U (η)ρ 0 0U† (η) ,
out { BS in ⊗| ih | BS }
scanning therelativephase between LO and signal from 0 to where the trace is taken overone ofthe output modes of
2π. The visibility between signal light field and LO is 88.5% the beam splitter. To see whether ρ (η) is similar to
out
incaseofthesqueezedvacuumfieldand90.3% incaseofthe
theactuallymeasuredoutputstateρ wecompute
LR-SPP mode. The data are normalized in a basis, where LR−SPP
the fidelity F(η) between the two states. The fidelity is
[xˆ,pˆ]=i. (b)and(f)Reconstructeddensitymatricesρin and
givenbyF(η)=tr ρ (η)ρ ρ (η) 1/2[15],
ρLR−SPP in the photon number basis obtained by applying { out LR−SPP out }
the maximum likelihood algorithm to the data presented in with 0 F(η) p1 and F(η) = p1 if and only if
≤ ≤
(a)and(e),respectively. ρhasbeenreconstructedforatrun- ρ (η) = ρ . In Fig. 3, we plot the fidelity F(η)
out LR−SPP
cated Hilbert space with a photon number of n=15. (c) and versus the transmission η of the beam splitter, which
(g)CalculatedWignerfunctionsW(X,P)forthedensityma- reaches F = 0.993 at maximum for η = 0.33. The large
trices shown in (b) and (f), respectively. (d) and (h) Noise
overlap between ρ (η = 0.33) and ρ are in ex-
powerofthedatasetpresentedin(a)and(f)(blacksolidline) out LR−SPP
cellent agreement with the measurements presented in
and calculated from the density matrices (red dashed line).
Fig. 1(c) and proves, that the plasmonic decoherence is
linear and thus can be simulated by a beam splitter in-
teraction.
Inthefollowingwejustifythisconclusionbyusingsim-
4
ple theoretical arguments. From the quantum mechan- tothelevelofsinglephotonsifweaddavacuumcontribu-
ical Maxwell equations the propagation of the field in tiontothe operatorequations. Thisconclusionisconsis-
an (electrically) polarizable medium may in general be tentwiththetheoreticalinterpretationinRef. [16]ofthe
described by experiments in Ref. [6], where it is concluded that the
polarization degrees of freedom leaves no ”which-way”
∂2 + 1 Eˆ = 1 ∂2 Pˆ, (1) informationin the solid. The presentwork,however,ex-
(cid:18)∂t2 c2∇×∇×(cid:19) −ǫ0∂t2 tends that conclusion by showing that also the presence
or absence of a photon leaves no ”which-way” informa-
where Eˆ is the electric field and Pˆ is the polariza- tion.
tion of the medium. We are here interested in the In conclusion, we have experimentally demonstrated
component at optical frequencies and split the electric the efficient plasmon-assisted propagation of squeezed
field into the positive and negative frequency compo- vacuum states in a gold waveguide. Through complete
nents Eˆ = Eˆ(+) + Eˆ(−), where the positive (negative) reconstruction of the density matrices of the input and
frequency component contains the photon annihilation output fields we found that the plasmonic propagation
(creation) operator. Similarly, we split the polarization can be described by a unitary beam splitting operation.
Pˆ = Pˆ(+)+Pˆ(−). The positive frequency component of The squeezing was therefore coherently transferred from
thepolarizationmaybeexpandedintermsoftheelectric thelightstatetotheplasmonicstateandbacktothelight
field state, solely degraded by vacuum noise. This demon-
∞ ∞ stratedrobustnessofcontinuousvariablequantumstates
m n
Pˆ(+) = cˆ ( Oˆ ) Eˆ(−) Eˆ(+) , (2) in plasmon propagation suggests that continuous vari-
mn i
mX=0nX=0 { } (cid:16) (cid:17) (cid:16) (cid:17) able quantum information processing based on surface
plasmons is feasible.
whereweincludethepossibilitythattheexpansioncoeffi-
We gratefully acknowledge support from the Vil-
cientcˆ maydependonasetofstateoperators Oˆ de-
mn { i} lum Kann Rasmussen Foundation, the Danish Research
scribingthe state ofthe polarizablemedium. During the
Council, and the EU project COMPAS.
propagation,the photonicexcitationsofthe electricfield
aremappedontothe(quasiparticle)excitationsofthepo-
larizable medium. The expansion coefficient c ( Oˆ )
mn i
{ }
thus gives access to information about the nature of the
excitationofthemediumand,e.g.,quasiparticleinterac- ∗ Electronic address: [email protected]
tions. Our experiment is performed in the low intensity † Electronic address: [email protected]
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5
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